Multi-scale constitutive model of human trabecular bone

The present study aims to formulate a new multiscale constitutive model of human trabecular bone. The trabecular bone was modelled as a nonlinear viscoelastic material. The viscoelastic effects of single trabeculae were considered by means of a hereditary integral in which stress depends on time and strain, while the elastic response was described by the hyperelastic Mooney-Rivlin model. The cuboid bone sample was extracted from the femoral head during the hip replacement surgery. The material constants in the constitutive equation were identified based on the stress relaxation test performed on the cuboid sample and the microindentation tests performed on trabeculae using the curve-fitting procedure. The microindentation tests were performed using a spherical tip instead of Vickers or Berkovich tip to minimize plastic effects during trabecular deformation. In order to validate formulated constitutive model, results from a FE simulation of stress relaxation test and uniaxial compression test were compared to the results of the corresponding experiments conducted on a macroscopic bone sample. Good agreement was observed between numerical and experimental results. The viscoelastic behaviour predicted by the proposed constitutive equation corresponds well to the response of human trabecular bone under various types of load conditions. This demonstrates the high ability of our constitutive model to simulate the behaviour of trabecular bone on a micro- and macroscopic scale. Thus, we conclude that the model, which was formulated for a single trabecula, can be successfully applied to simulate mechanical behaviour of the tissue in a macroscale.